Re: HoldAll for Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg97986] Re: HoldAll for Integrate
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 27 Mar 2009 05:35:12 -0500 (EST)
- References: <gqfknb$kht$1@smc.vnet.net>
Hi,
compare
x = 10;
SetAttributes[Integrate, HoldAll];
Trace[Block[{x}, Integrate[x^2, x]]]
with
Trace[Integrate[x^2, x]]
and you see, that x^2 is evaluated to 100 but
x is preserved, than 100 dx is computed to 100*x
and than x->10 is substituted again to give
1000
Regards
Jens
Tammo Jan Dijkema wrote:
> The following commands yield unexpected output:
>
> x=10;
> Integrate[x^2, {x,0,1}]
>
> That is because Integrate does not have attributes HoldAll, so that the
> second command will be interpreted as Integrate[100, {10,0,1}] which is
> not a command that Integrate can work with (so a warning message is
> returned).
>
> However, I can add the attribute HoldAll to Integrate myself:
>
> SetAttributes[Integrate, HoldAll];
>
> I'm not very sure what to expect when now trying the same experiment
> (the correct answer 1/3 would be nice), but the actual output surprised
> me:
>
> x=10;
> Integrate[x^2, {x,0,1}]
>
> Yields as output: 0 (without any warnings). Could anyone explain why I
> should have expected this result?
>
> On a side note, I found a similar in the Tech Support column of the
> Mathematica Journal Volume 6, Issue 2, by Carl Roy. He tried the
> integral without limits:
>
> x=10;
> SetAttributes[Integrate, HoldAll];
> Integrate[x^2, x]
>
> In the journal, the output 1000/3 is mentioned, whereas in Mathematica
> 7.0.1 this outputs 1000.
>
> Again, does anyone understand this?
>
> Regards,
>
> Tammo Jan Dijkema
>
>